   Chapter 21, Problem 66E

Chapter
Section
Textbook Problem

# Use the data in Appendix 4 for the following.a. Calculate  ΔH° and ΔS° for the reaction 3 Fe 2 O 3 ( s ) + CO ( g ) → 2 Fe 3 O 4 ( s ) + CO 2 ( g ) that occurs in a blast furnace.b. Assume that  ΔH° and ΔS° are independent of temperature. Calculate  ΔG° at 800.°C for this reaction.

(a)

Interpretation Introduction

Interpretation: The reaction between Fe2O3 and CO is given. The value of ΔH,ΔS and ΔG are to be calculated for the given options.

Concept introduction: The expression for ΔH is,

ΔH=npΔH(product)nfΔH(reactant)

The expression for ΔS is,

ΔS=npΔS(product)nfΔS(reactant)

The expression for standard Gibbs free energy, ΔG, is,

ΔG=ΔHTΔS

To determine: The value of ΔH and ΔS for the given reaction.

Explanation

Explanation

The reaction that takes place is,

3Fe2O3(s)+CO(g)2Fe3O4(s)+CO2(g)

Refer to Appendix 4.

The value of ΔH(kJ/mol) for the given reactant and product is,

 Molecules ΔH0(kJ/mol) Fe3O4(s) −1117 CO2(g) −393.5 Fe2O3(s) −826 CO(g) −110.5

The formula of ΔH is,

ΔH=npΔH(product)nfΔH(reactant)

Where,

• ΔH is the standard enthalpy of reaction.
• np is the number of moles of each product.
• nr is the number of moles each reactant.
• ΔH(product) is the standard enthalpy of product at a pressure of 1atm.
• ΔH(reactant) is the standard enthalpy of reactant at a pressure of 1atm.

Substitute all values from the table in the above equation.

ΔH=npΔH(product)nfΔH(reactant)=[2(1117)+2(393.5){3(826)+(110

(b)

Interpretation Introduction

Interpretation: The reaction between Fe2O3 and CO is given. The value of ΔH,ΔS and ΔG are to be calculated for the given options.

Concept introduction: The expression for ΔH is,

ΔH=npΔH(product)nfΔH(reactant)

The expression for ΔS is,

ΔS=npΔS(product)nfΔS(reactant)

The expression for standard Gibbs free energy, ΔG, is,

ΔG=ΔHTΔS

To determine: The value of ΔG at 800°C for the given reaction.

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